Proceedings ofISCIT2005

The Application of Fuzzy Control Strategy inElectro-hydraulic Servo System

Junpeng Shao, Lihua Chen, Yajuan Ji, Zhibin SunDepartment of Mechanical Power Engineering

University of Science and Technology, Harbin, Heilongjiang Province, ChinaTel: +86-0451-86390501, +86-013604847986

E-mail: Sjp566@sina.com, Meryl2008@tom.com, zhibin2l @163.com

Abstrct- This paper presents a fuzzy tracking controlmethodology for electro-hydraulic servo system from theviewpoint of industrial application and implementation.Since the hydraulic control systems always have the highnonlinearity and uncertain dynamics, the simple linear ornonlinear differential equations can not sufficiently representcorresponding practical system. And many conventionalcontrol methods based on mathematical models are limited intheir abilities to improve the tracking performance. Thesolution in this study is to develop a new nonlinear hybridcontroller composed of a classical PID controller and a fuzzycontroller based on self-adjusting modifying factor, whichgreatly improves the robustness, the dynamic and staticproperties of the system. Additionally, the fuzzy switchingmode is employed to avoid the undesirable disturbancescaused by the switchover between the two control methods.The proposed fuzzy controller shows excellent robustnessagainst variations of system parameters and externaldisturbances through a series of simulation studies. Finally,by experiments on a practical electro-hydraulic servo testbench, the effectiveness of this control scheme is verified bycomparison with the classical PID or fixed fuzzy controller.The research results show that the hybrid fuzzy PIDcontroller has good performance in real time application.Keywords: electro-hydraulic servo system, hybrid fuzzy PID

control, fuzzy switching mode, Self-tuning gene fuzzy control

I. INTRODUTION

The application of hydraulic actuation to heavy-dutyequipment reflects the ability of the hydraulic circuit totransmit larger forces and to be easily controlled.Especially the electro-hydraulic servo system is perhaps themost important system for position servo applicationsbecause it takes the advantages of both the large outputpower of traditional hydraulic systems and the rapidresponse of electric systems. However, there are alsomany challenges in the design of electro-hydraulic controlsystems. For example, they are the highly nonlinearphenomena such as fluid compressibility, the flow-pressurerelationship and dead band due to the internal leakage andhysteresis, and the any uncertainties of hydraulic systemsdue to linearization. Therefore, it seems to be quitedifficult to perform a high precision servo control by usinglinear control methods.

In order to accomplish more accurate and faster control

system an effect of modeling error or uncertainties must beconsidered. However, the fuzzy logic controller (FLC) isbased on a set of linguistic control rules related by the dualconcepts of fuzzy implication and the compositional rulesof inference. Since the methodology of FLC provides analgorithm which converts the linguistic control strategybased on expert knowledge into an automatic controlstrategy, it appears particularly useful in cases whereprocesses are too complex for analysis by conventionalcontrol techniques, or where the available sources ofinformation are inexact or uncertain.

Although several fuzzy control schemes have beenapplied to actual systems and have achieved greatimprovements, transient and steady control performance islimited. It has been seen that this behavior is, in principle,identical to that of a PD-type controller which yields a finitesteady-state error for a "type 0" system and has no poles onthe origin of the complex s-plane. One trend appears in thedirection of designing an FLC systematically and assuringstability with the aid of conventional control theories.

This paper presents a fuzzy PID (proportional, integral,derivative) controller by combining the merits of fuzzylogic and conventional linear control theory. The fuzzycontroller is used to control the system when the piston isfar away from the target position while the PID controller isapplied when the piston is near the desired position. Asexpected, the classical PID control method is taken intoconsideration to eliminate the steady-state error of thesystem. Additionally, the fuzzy switching mode isemployed to avoid the undesirable disturbances caused bythe switchover between the two control methods. Andthrough the use of an on-line self-regulating scaling factor,the obtained fazzy controller lead the control system toyield responses with fast rise times and small overshoots aswell as short settling times.

II. MATHEMATICAL ANALYSIS AND MODELBUILDING OF ELECTRO-HYDRAULIC SERVO

SYSTEMThe design of controllers for nonlinear electro-hydraulic

servo system has been extensively studied in recent years.A laboratory experimental electro-hydraulic servo systemis shown in Fig. 1, where the mass-spring system is the

0-7803-9538-7/05/$20.00©2005 IEEE 159

fii

5

Fig. I The sinplified chart oftheelectro-hydraulic servo test bench

external load and is driven by a hydraulic cylindercontrolled by a servo valve. The objective is to keep thedisplacement xp of the cylinder following a desiredtrajectory xv as possible, regardless of operating points.

It's assumed that the servo valve is a zero lapquadrilateral sliding spool valve and the compressibility ofthe liquid is neglected. Since the system has the lowest freefrequency and stability when the piston is in the middle ofthe valve, as Fig.2 shows, the entire system equations aredescribed as follows.

A. The linearizedflow equation ofthe servo valveThe relation between the servo valve spool displacement

xV and the load flow Q I is governed by the orifice law:

Q, =cdwx,-PF-(x,,/lx, V)ijp) (1)Where Q, is the load flow of the servo valve. w is theservo valve area gradient. Cd is the discharge coefficientof the cylinder. p is the oil density, and P. is the supplypressure. pL = P, - P2 is the load pressure drop causedby the fluid cylinder. xv is the displacement of spool inthe servo valve.The values of the valve coefficients change along with

the varying chamber pressures in respect of movements.However, since the position control system alwaysperforms around the original point at which the system hasthe lowest stability, the above equation can be linearizedaround this key point. And the increment is equal to thevariable at the origin. So the flow equation can belinearized as follows:

QL = kqx,, - K,PL (2)Where Kq is the valve flow gain that varies under different

Fig.2 The schematic structure of thecylinder controlled by the valve

operation points. Kc is the valve pressure gain underdifferent operating point.B. Theflow continuity equation ofthe cylinder chamber

QL = AP x P+ C,PL + (V, /4,/ e)PL (3)Where AP is the pressure area in the actuator. xp is thedisplacement of cylinder shaft. C, is the leakagecoefficient of cylinder. V, is the effective system oilvolume. ,lie is the oil effective bulk module.

C. Theforce balance equationfor the cylinder

Fg = APPL = Mt xp + Bp xP + KSxP + FL (4)Where Fg is the driving force of the cylinder. Mt is theeffective system mass. Bp is the coefficient of viscousfriction. 14 is the elastic load stiffness. FL is the externaldisturbance.D. The simplified transferfunction ofthe servo valveAs the fluid free frequency ,, h is higher than 50Hz, the

servo valve can be regarded as a second-order system.K,,,G,(s) = Q,/IA = K,1(S |w. )+ (24,,/w,s)+l] (5)Where Ksv is the ratio of the rated flow and the current flow.w,, and S. are respectively the free frequency and thedamping coefficient of the servo valve.E. The model building ofthe position servo system

Fig. 3 shows the block diagram of the electro-hydraulicservo system. Where Ka is the servo amplifier gain, and uis the servo valve control input signal, and K. = K, + C, iSthe total flow-pressure coefficient. Gl(S) is the transfer

160

Fig. 3 The block diagram of the electro-hydraulic servo system

function of the servo valve. G2(S) is the transfer functionof the cylinder. H(S) is the input element of the externalload. Here since the response frequency of the differentialtransformer type displacement sensor is far bigger than thatof the system, the transfer function of the sensor is regardedas a proportional component and the gain is K[.

GI (S) = KsG(s) = KjI/[(S2/w,.,2)+ (2/,/Wj) + 1] (6)G2 (S) = (l/A )/ + (KceK/A2 )I(s2/wh2 )+ (2ih /Wh )+ 1 (7)

h = (Kce/Ap)(eM , lYt )X + (BP/4Ap XV /IeM I ))

ch 4=/3Ap/M,VtH (s) = (Kce/Ap)[1 + (VJ /4/JeKce)S] (8)

III. DESIGN OF THE FUZZY-LOGIC CONTROLLER

The proposed fuzzy controller is shown in Fig. 4. Asillustrated in this diagram, the hybrid controller iscomposed of a classical PID controller and a fuzzycontroller based on self-adjusting modifying factor. Thefuzzy controller is used to control the piston when the pistonis far away from the target position, and the PID controlleris applied when the piston is near the desired position.

Fuzzy control theory involves fuzzification, a fuzzy rulebase generalized from experts' experience, fuzzy inferenceand defuzzification. However, self-adjustment of thefuzzy control rules is the key factor to improve thecontroller's performance. On this basis, the modifyingfactor's fuzzy number model is employed to regulate thefuzzy control rules on-line in this study.The fuizzy inputs (error and the change rate of error) are

classified into seven equal-span triangular membershipfunctions scaled within a range of-6 to 6. Where NB, NM,NS, 0, PS, PM, PB are negative big, negative medium,negative small, zero, positive small, positive medium and

Fuzzy conirovl blocwk

positive big. Fig. 5 shows the membership functions offuzzy input variables. The outputs (a) is partitionedby themembership function set M(a) = {VB,B,M,S,VS }. WhereVB, B, M, S and VS are very big, big, zero, small and verysmall. And the scaling factors GE, GEC, GU and Gi areemployed to map the variables into the universe ofdiscourse, which are optimized by ITAE integralperformance indexing.

The proposed rule bases can be described as follows:U = aE + ( 1 - ii)EC> (9)

Since the modifying factor 'a' can directly reflect theweighting degree of the error (E) and the change of error(EC), it faithfully shows the characteristics of the operator'sthought in controlling. Thus the main task of on-lineregulating control rules can be transformed to regulate themodifying factor. Based on expert experience and controlengineering knowledge, the fuzzy model of on-lineself-tuning modifying factor is shown in Table I.

Interpolation method is used in the modifying factorfuzzy number model to improve the control rules, whichultimately removes the quantization error and regulatingdead space.

NWB ~NM NS 0 PS PM P

05

-4 -I 0 4

Fig. 5 The membership functions of fuzzy input variables

Table I The fuzzy model of on-line self-tuning modifying factor

E NB NM NS 0 PS PM PB

NB VB VB VB VB VB VB VBNM VB VB VB VB B M MNS VB VB B B M S SO Vs Vs Vs M Vs Vs VsPS S S M B B VB VBPM M M B VB VB VB VBPB VB VB VB VB VB VB VB

-I

Fig. 4 The hybrid controller of fuzzy and PID control

161

0 f:E, EC

According to Taylor binary function, when E <E<E,,and E£j < EC <ECj+l, 'a' can be approximately describedas follows:or = f(E,EC) +(afcC,£a)/aE + af(-E )/aEC`5EC =f(E,EC) + (f(E,+1,EC j) )/(Ei+l- r), E-E )+ f ,,ECj+1) - f (E, ,EC£j ))/ECj+1 - ECj)JE - Ej)'a = Pij+ i+ (E)(,j+1,j-1ij) + pj+1 (EC )(i,j+l - -,j)

j+1(E) = (E - Ei)/(Ei+l - Ej) (10)

Pj+1 (EC) = (EC - EC7j)/(EC-j+l - EC-j)The defuzzification is to transform the control signal into

an exact control output. In the defuzzification, the methodof center of gravity is used.

y=-WjBj (11)i-l i=l

Where y is the output of the fuzzy controller. w i is thedegree of firing of the ith rule. B i is the centroid of theconsequent fuzzy subset of the ith rule.Furthermore, fuzzy switchover mode is employed to

avoid the undesirable disturbances caused by theswitchover between fuzzy and PID control methods. Thefuzzy inference rule is as follows:

IF E(k) is SE and EC(k) is SEC THEN "4output" is UPIDElse "output" is U

Where UPID is that ofthe linear PID control and Uf"is theoutput of the fuzzy control. SE and SEC are respectivelythe switching membership functions of the fuzzy variable Eand EC, which is shown in Fig. 6. L can be set by theexecution area of the fuzzy switchover.

Fig. 6 The member functions of fuzzy input variablesThe output actuating signal of the fuzzy controller isdefined as: U(k) = 4p]* UpID + pf.rjyU fiY

IPID = psE (E(k)) /sEC (EC(K)), yfa,zz=1l-pID (12)

IV. COMPUTER SIMULATION RESULTSIn order to assure the effectiveness of the nonlinear fuzzy

PID controller, computer simulations were executed for theelectro-hydraulic servo system which was expressed as theblock diagram in Fig. 3. To verify the availability of thedesigned controllers in practical implementation, differentsinusoidal disturbances are introduced into the system

outputs to simulate the corresponding absorptivity of theelectro-hydraulic system. The sampling frequency wasselected as 1000Hz and the algorithm ode45 was applied tothe calculation process.The main parameters for the mathematical model of the

electro-hydraulic servo system are listed as follows. Thedisplacement sensor gain Kf is 50V/m. The servo amplifiergain Ka is 0.016A/V. The elastic load stiffness K; is 0.The servo valve gain Ksv is 0.00579 m3/S. A. The effectivesystem oil volume V, is 2 x 10-4m3 . The pressure area in theactuator Ap is 1 x 10 -3 m 2 The effective systemmass Mt is 25Kg. The oil effective bulkmodule ,8e is 7Xl18Pa The leakage coefficient ofcylinder Kce is 4.8 x 1 0-12m3/IS PaAccording to the fuzzy controller proposed above, the

system was respectively modeled by the toolbox ofMATLAB. With the same input of unit step signals, theoutputs of systems with different controllers were plottedfor comparison. The time axes for simulation results wereplotted in terms of seconds converted from discrete indexnumbers. Since the feedback ratio is 50V/m, the desiredoutput is 0.02m. As is shown in Fig. 8, the hybrid of fuzzyand PID controller exhibits a good unit step response withnearly zero overshoot, faster rising time and moresatisfactory settling time than that of the conventional fuzzycontrol and the PID control system. Especially the responseof the system with the conventional fuzzy controller showsgreat steady-state error.

With the disturbance of 5000sin6wt (N) introduced to thesystem, the proposed fuzzy controller above turns out anonlinear controller and exhibits a good stable transient andsteady state performance without regard to a point that agiven plant is linear or nonlinear, as is shown in Fig. 9.And the conventional fuzzy controller also performs wellon suppressing the error caused by the disturbance, but itleads to mild agitation around the steady-state.The electro-hydraulic servo systems usually have some

highly nonlinear phenomena such as fluid compressibility,the flow-pressure relationship and dead band due to theinternal leakage and hysteresis, and the many uncertaintiesdue to linearization, which have certain effects on theparameters of the studied system. To further evaluate thecontrol performance of the proposed fuzzy controller, theamplification coefficient of the system's open loop transferfunction was doubled. As was expected, the proposedfuzzy controller has advantage in improving the robustness,the dynamic and static properties of the system. Thesimulation results are given in Fig. 10.

It was also known that in the design the combination ofGE, GEC and GU are based on the given input/outputrelation. They must be selected carefully and be modifiedstep by step with small incremental values to obtain stabledesired output in simulation experiments.

162

V. EXPERIMENTAL RESULTS AND DISCUSSIONS

To verify the effectiveness of the proposed fuzzycontrollers in practical application, real-time control studywas performed on the electro-hydraulic servo test bench(Fig. 7). Generated by the computer, the input signal wassent to the servo amplifier by the DAS card (PCL-818HD).Then the amplified signal was passed to the servo valvewhich controls the hydraulic cylinder to move. Thedisplacement of the piston was fed back through thedisplacement sensor. At last the signal was send back tothe computer to be processed.

The control program, which is the basic of experiment,include modules of generating input signal, controlling thedata acquisition card, realization of the control algorithm,data saving etc..To evaluate the position control performance of the

proposed controllers, the desired tracking inputs arerespectively set to be step and sinusoidal signals. Thecvlinder trackino, ciitnvuts to the sten innuts of( 0(Y i nirp

shown in Fig. 12. Compared with the PID control strategy,the fuzzy PID controller shows advantage in improving thesettling time of the practical test bench. Though thesystem with the conventional fuzzy controller also exhibitsfaster rising time, it has mild agitation around thesteady-state position. Since the simple linear or nonlineardifferential equations can not sufficiently representcorresponding practical system, certain parameters of thecontrollers are slightly amended in the experiments. Thenthe response time of the practical test bench is a littledifferent from that of the emulation results, the reason ofwhich includes linearization of the practical system,selection of the parameters' values and calculation errorsetc.. However, the practical experimental results by andlarge accord with the emulation.

For a reference sinusoidal input, x=l sinzrt (m), to the testbench, Fig. 11 depict the corresponding tracking responsesand its errors. Compared with the response curves of PIDcontroller, the fuzzy controller above possesses aremarkably better tracking performance.

Comparson of the step responses

0.02

0.018

0.01

- 0.01IDa

o 0.01

_ 0.0

0.00

0.00

0.00

0.00

Fig 7 The electro-hydraulic servo test bench.03 ll ll

025 - --------

,--- F

011

.I -q- - - --- -.

X} ~~~~~I

0 - -.- - -Csmmand Input5 R7 _ _ _1_ _ _ _ -----ID Control

- Fuzzy Control

O-

F - The Hybrid of Fuzzy and PID Control0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (sec)

6

4

2

8

6

4

2

0,

0.018

0.016

0.014

E 0.012

2 0.01

0.008

0.006

0.004

0.002

lI .

IIoF__ - I-- --

1It F

--1 --r--

.1____ 1___L

F

I

LL...I

- Command Input-- PID Control- Fuzzy Control- The Hybnd of Fuzzy and PID Control

0 0.02 0.04 1.06 0.08 0.1 0.12 0.14 0.16 0.11Time (sec)

Fig 8 Comparison ofthe unit step responses

I/

---- _A - _ _ _ _

I~-l--I-.~T~ -n~~~ -

NI:-,- _l-__ ---_r_

IIIL_ I_ J - _ _ L _ _ _I_ T.I

T --Fl---r 1-l.______L_I

TI

Command InputPID ControlFuzzy ControlThe Hybrid of Fuzzy and PID Control

U U.01 U.02 U.05 0.04 0.06 0,07 0.06 0.09 0.1Time (sec)

Fig 9 Comparison of the unit step responses (with disturbance of 5000sin67rt(N)) Fig 10 Comparison of the unit step responses (with parameter's change )

163

0.

0.0

22

I

0.

0.0

J9

0.0

I11:

II.

I

t'i-_L _ _-_._ __

_ R-L t4

I _ -

.1

10 11 12

it_____l___- _

----&-J

L- - -IL

vj- - ---- S-At - -i

5 Plant. RPID Control

The Hybrid of Fuzzy and PID Control13

Time(sec)14 15

Fig 11 Comparison of the sinusoidal tracking responses and its errors of the practical test bench

a)

205

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Time (sec)

0.8 0.9

Fig 12 Comparison of the step tracking responsesofthe practical test bench

VI. CONCLUSION

In this paper, a hybrid of fuzzy and PID controller has beensuccessfully presented and applied to the electro-hydraulicservo test bench. While it's easy to design controllers for thelinear or nonlinear time invariant systems, it is more or lesshard to design and requires careful tuning of controllerparameters for nonlinear systems. On the other hand,traditional modeling techniques are rather complex and timeconsuming. However, a fuzzy controller can be the solutionbecause it compensates for the shortcomings of the model,which cannot be estimated when modeling. The robustnessand effectiveness were verified through the computersimulations and experiments. With this new controller, thetracking error has been effectively reduced and the chatteringphenomenon has been successfully suppressed. From the

laboratory testing, it's concluded that, for trackingperformance ofthe servo system, the fuzzy PID controller isbetter than the linear PID controller and the conventionalfuzzy controller.

REFERENCES[1] S. Ma, J. Ye, J. Li, "Hydraulic servo control system," Coal Industry

Press, 1990.[2] W. Zhang, X. Yang, "Fuzzy control theory and application," Xibei

Institute University Press, 2001.[3] X. Wen, L. Zhou, D. Li, C. Be, "The analysis and application ofthe

fuzzy logic toolbox," Science Press, 2001.[4] G. Zhang, N. Li, "MATLAB simulation technology and

application," Qinghua University Press, 2003.[5] H. Xue, "Computer control techniques," Xian: Electron Scientific

and Technical University Press, 2004.[6] Li. Wang, "A course in fuzzy systems and control," Qinghua

University Press, 2003.[7] H. Liu, S. Li, T. Chai, "A new method of designing the hybrid

controller of fuzzy-PID control and its application in electric powerplant," Power Engineering, January, 2004

[8] Zhang, D.W., "Application of hybrid fuzzy PID control to auxiliaryworkpiece table," Advances in Materials Manufacturing Science andTechnology, v 471- 472, 2004, pp. 264-268.

[9] Zhang, Deyin, "Hybrid fuzzy control of robotics systems," IEEETransations on Fuzzy Systems, vol. 12, December, 2004, pp.755-765.

[10]Zhao, Yingkai, "Intelligence control of nonlinear systems based onMatlab simulation and the real-time control platform," Proceedingsofthe World Congress on Intelligent Control and Automation, vol. 1,2002, pp.786-789

[l]Cupec, Robert, "Self-tuning controller based on process fuzzymodel," Computational Intelligence and Applications, 1999, pp.187-192.

[12]Butkiewicz, B.S., "System with hybrid fuzzy-conventional PIDcontroller," Proceedings of the IEEE International Conference onSystems, vol. 5, 2000, pp3705-3709.

[13]Woo Z, Chung H, Lin J, "A PID type fuzzy controller with selftuning scaling factors," Fuzzy Sets Syst, 2000, pp 321-326.

[14]B.Zhu, R. Wu, R. Xiong, "Research for the fuzzy-immune-PIDcontrol of the electro-hydraulic servo system," China MeasurementTechnology, no.1, 2004.

164

20

15

10

0)

cn205

Time (sec)

5

0

-5

E

0wti

-10

-15

-20

16

L --- - Command Input. .; PID Control

Fuzzy ControlI --- The Self-tuning Fuzzy PID Control

- - - - - I

L------J1.1